From any ISBN code we can calculate a `check total' by multiplying the digits
in the code by 1, 2, 3, <font face="symbol">¼</font
> in order and adding these products. For example 0 <font face="symbol">-</font
>04 <font face="symbol">-</font
> 823208 <font face="symbol">-</font
> 4 gives



<br clear="all" /><table border="0" width="100%"><tr><td>
<table align="center"><tr><td nowrap="nowrap" align="center">
(1<i>x</i>0) + (2<i>x</i>0) + (3<i>x</i>4) + (4<i>x</i>8) + (5<i>x</i>2) + (6<i>x</i>3) + (7<i>x</i>2) + (8<i>x</i>0) + (9<i>x</i>8) + (10<i>x</i>4) = 198.</td></tr></table>
</td></tr></table>




<p/>
Try this for yourself with any ISBN number and the check total will always be
divisible by 11. This calculation is used to check that the book number has
been copied down accurately and thus to avoid errors in placing orders. 


<p/>
This solution is from Abbas Tejani, age 11, Jack Hunt School,
Peterborough. Well done Abbas! 


<p/> 
What I noticed is that all the answers have one thing in common. They are all
divisible by 11. 


<p/>
In the ISDN code 





<br clear="all" /><table border="0" width="100%"><tr><td>
<table align="center"><tr><td nowrap="nowrap" align="center">
0 <font face="symbol">-</font
> 947?95 <font face="symbol">-</font
> 24 <font face="symbol">-</font
> 3 </td></tr></table>
</td></tr></table>




<p/>
the question mark must be replaced by the number 7. This is the smallest
number that gives a check total that is exactly divisible by 11. See the
working below. 




    


<table border="1" cellpadding="5" cellspacing="0">
<tr>
<td>Multiplier</td>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
<td>9</td>
<td>10</td>
<td rowspan="2">Total:<br /></td>
</tr>
<tr>
<td>ISBN Number</td>
<td>0</td>
<td>9</td>
<td>4</td>
<td>7</td>
<td>7</td>
<td>9</td>
<td>5</td>
<td>2</td>
<td>4</td>
<td>3</td>
<td></td>
</tr>
<tr>
<td>Product</td>
<td>0</td>
<td>18</td>
<td>12</td>
<td>28</td>
<td>35</td>
<td>54</td>
<td>35</td>
<td>16</td>
<td>36</td>
<td>30</td>
<td>264 = 24 x 11</td>
</tr>
</table>